Methods for detecting a magnetic field acting on a magneto-optical detect center having pulsed excitation

ABSTRACT

A method for detecting a magnetic field acting on a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers may include controlling an optical excitation source and an RF excitation source to apply a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receiving a light detection signal from an optical detector based on an optical signal emitted by the NV diamond material due to the pulse sequence, measuring a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, measuring a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, and computing a measurement signal based on the measured first and second values. Such method may further may further comprise measuring a third value of the light detection signal at a signal period, the signal period being after the first reference period and before the second reference period. Such method may further comprise computing the measurement signal based on a difference between the average of the first and second values and the third value.

CROSS-REFERENCE TO RELATED PATENT APPLICATION

This application is a Continuation of U.S. patent application Ser. No. 15/003,590, filed Jan. 21, 2016, which claims the benefit of priority to U.S. Patent Application No. 62/107,289, filed Jan. 23, 2015, the entire contents of which are incorporated by reference herein in their entirety.

FIELD

The present disclosure generally relates to magnetic detection systems, and more particularly, to measurement and signal processing methods for a magnetic detection system.

BACKGROUND

A number of industrial applications including, but not limited to, medical devices, communication devices, and navigation systems, as well as scientific areas such as physics and chemistry can benefit from magnetic detection and imaging. Many advanced magnetic imaging systems can operate in limited conditions, for example, high vacuum and/or cryogenic temperatures, which can make them inapplicable for imaging applications that require ambient conditions. Furthermore, small size, weight and power (SWAP) magnetic sensors of moderate sensitivity, vector accuracy, and bandwidth are valuable in many applications.

Atomic-sized nitrogen-vacancy (NV) centers in diamond have been shown to have excellent sensitivity for magnetic field measurement and enable fabrication of small magnetic sensors that can readily replace existing-technology (e.g., Hall-effect) systems and devices. The sensing capabilities of diamond NV (DNV) sensors are maintained at room temperature and atmospheric pressure, and these sensors can be even used in liquid environments (e.g., for biological imaging). DNV sensing allows measurement of 3-D vector magnetic fields that is beneficial across a very broad range of applications, including communications, geological sensing, navigation, and attitude determination.

SUMMARY

According to certain embodiments, a system for magnetic detection may include a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers, a radio frequency (RF) excitation source configured to provide RF excitation to the NV diamond material, an optical excitation source configured to provide optical excitation to the NV diamond material, an optical detector configured to receive an optical signal emitted by the NV diamond material, a magnetic field generator configured to generate a magnetic field applied to the NV diamond material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a first pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receive a first light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the first pulse sequence, measure a first value of the first light detection signal at a first reference period, the first reference period being before a period of the first light detection signal associated with the two RF excitation pulses of the first pulse sequence provided to the NV diamond material, measure a second value of the first light detection signal at a second reference period, the second reference period being after the period of the first light detection signal associated with the two RF excitation pulses of the first pulse sequence provided to the NV diamond material, compute a first measurement based on the measured first and second values of the first light detection signal, control the optical excitation source and the RF excitation source to apply a second pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receive a second light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the second pulse sequence, measure a first value of the second light detection signal at a first reference period, the first reference period being before a period of the second light detection signal associated with the two RF excitation pulses of the second pulse sequence provided to the NV diamond material, measure a second value of the second light detection signal at a second reference period, the second reference period being after the period of the second light detection signal associated with the two RF excitation pulses of the second pulse sequence provided to the NV diamond material, and compute a second measurement based on the measured first and second values of the second light detection signal. The first measurement may be based on a high resonance frequency of the NV diamond material, and the second measurement may be based on a low resonance frequency of the NV diamond material.

According to one aspect, a high resonance frequency and a low resonance frequency may be resonance frequencies associated with an axis of an NV center of the NV diamond material.

According to one aspect, a controller may be further configured to compute a change in an external magnetic field acting on the NV diamond material based on the first and second measurements.

According to other embodiments, a system for magnetic detection may include a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers, a radio frequency (RF) excitation source configured to provide RF excitation to the NV diamond material, an optical excitation source configured to provide optical excitation to the NV diamond material, an optical detector configured to receive an optical signal emitted by the NV diamond material, a magnetic field generator configured to generate a magnetic field applied to the NV diamond material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receive a light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the pulse sequence, measure a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, measure a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, and compute a measurement signal based on the measured first and second values.

According to one aspect, a controller may be further configured to measure the first value and the second value based on an average of values of the light detection signal within the first reference period and the second reference period.

According to one aspect, a controller may be further configured to compute the measurement signal based on the average of the first value and the second value.

According to one aspect, a controller may be further configured to measure a third value of the light detection signal at a signal period, the signal period being after the first reference period and before the second reference period.

According to one aspect, a controller may be further configured to compute the measurement signal based on a difference between the average of the first and second values and the third value.

According to one aspect, a first reference period may be associated with one of the two optical excitation pulses and a second reference period may be associated with the other of the two optical excitation pulses.

According to other embodiments, a system for magnetic detection may include a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers, a radio frequency (RF) excitation source configured to provide RF excitation to the NV diamond material, an optical excitation source configured to provide optical excitation to the NV diamond material, an optical detector configured to receive an optical signal emitted by the NV diamond material, a magnetic field generator configured to generate a magnetic field applied to the NV diamond material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a first pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receive a first light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the first pulse sequence, compute a first measurement based on the first light detection signal, control the optical excitation source and the RF excitation source to apply a second pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receive a second light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the second pulse sequence, and compute a second measurement based on the second light detection signal. The first measurement may be based on a high resonance frequency of the NV diamond material, and the second measurement may be based on a low resonance frequency of the NV diamond material.

According to one aspect, a high resonance frequency and a low resonance frequency may be resonance frequencies associated with an axis of an NV center of the NV diamond material.

According to one aspect, two RF excitation pulses of the first pulse sequence may be applied at a frequency detuned from the high resonance frequency of the NV diamond material.

According to one aspect, two RF excitation pulses of the second pulse sequence may be applied at a frequency detuned from the low resonance frequency of the NV diamond material.

According to one aspect, a controller may be further configured to compute a change in an external magnetic field acting on the NV diamond material based on the first and second measurements.

According to other embodiments, a system for magnetic detection may include a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers, a radio frequency (RF) excitation source configured to provide RF excitation to the NV diamond material, an optical excitation source configured to provide optical excitation to the NV diamond material, an optical detector configured to receive an optical signal emitted by the NV diamond material, a magnetic field generator configured to generate a magnetic field applied to the NV diamond material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a plurality of pulse sequences to the NV diamond material, each of the plurality of pulse sequences comprising two optical excitation pulses and an RF excitation pulse, wherein a time period of application of the RF excitation pulse may be varied among each of the plurality of pulse sequences. The controller may be further configured to receive a plurality of light detection signals from the optical detector based on an optical signal emitted by the NV diamond material due to the plurality of pulse sequences, measure a first value of each of the plurality of light detection signals at a first reference period, the first reference period being before a period associated with the RF excitation pulse of each of the plurality of pulse sequences, measure a second value of each of the plurality of light detection signals at a second reference period, the second reference period being after the period associated with the RF excitation pulse of each of the plurality of pulse sequences, compute a plurality of measurement signals based on the plurality of measured first and second values, and calculate a frequency of the plurality of measurement signals.

According to one aspect, a frequency may be a resonant Rabi frequency.

According to one aspect, an RF excitation source may be a microwave antenna.

According to one aspect, a microwave antenna may be a small loop antenna.

According to one aspect, a small loop antenna may comprise a loop having a diameter of about 2 mm.

According to one aspect, a microwave antenna may be configured to provide a microwave power of at least 10 watts.

According to one aspect, a controller may be configured to apply one of the two optical excitation pulses, followed by the RF excitation pulse, and followed by the other of the two optical excitation pulses during each of the plurality of pulse sequences.

According to one aspect, a controller may be configured to apply a window between the one of the two optical excitation pulses and the RF excitation pulse during each of the plurality of pulse sequences, the window being a time period in which no excitation or optical excitation is applied to the NV diamond material.

According to one aspect, a controller may be further configured to identify a first minimum of the plurality of measurement signals.

According to other embodiments, a system for magnetic detection may include a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers, a radio frequency (RF) excitation source configured to provide RF excitation to the NV diamond material, an optical excitation source configured to provide optical excitation to the NV diamond material, an optical detector configured to receive an optical signal emitted by the NV diamond material, a magnetic field generator configured to generate a magnetic field applied to the NV diamond material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a plurality of pulse sequences to the NV diamond material, each of the plurality of pulse sequences comprising two optical excitation pulses and two RF excitation pulses, wherein a time period between application of the two RF excitation pulses is varied among each of the plurality of pulse sequences, receive a plurality of light detection signals from the optical detector based on an optical signal emitted by the NV diamond material due to the plurality of pulse sequences, measure a first value of each of the plurality of light detection signals at a first reference period, the first reference period being before a period associated with the RF excitation pulse of each of the plurality of pulse sequences, measure a second value of each of the plurality of light detection signals at a second reference period, the second reference period being after the period associated with the RF excitation pulse of each of the plurality of pulse sequences, compute a plurality of measurement signals based on the plurality of measured first and second values, and calculate a decay time of the plurality of measurement signals.

According to one aspect, two RF excitation pulses of each of the plurality of pulse sequences may be applied at a frequency of about 10 MHz.

According to other embodiments, a system for magnetic detection having a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers may include means for providing RF excitation to the NV diamond material, means for providing optical excitation to the NV diamond material, means for receiving an optical signal emitted by the NV diamond material, means for generating a magnetic field applied to the NV diamond material, means for applying a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, means for receiving a light detection signal based on an optical signal emitted by the NV diamond material due to the pulse sequence, means for measuring a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, means for measuring a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, and means for computing a measurement signal based on the measured first and second values.

According to other embodiments, a method for detecting a magnetic field acting on a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers may include controlling an optical excitation source and an RF excitation source to apply a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receiving a light detection signal from an optical detector based on an optical signal emitted by the NV diamond material due to the pulse sequence, measuring a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, measuring a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the NV diamond material, and computing a measurement signal based on the measured first and second values.

According to one aspect, a method may further comprise computing the measurement signal based on the average of the first value and the second value.

According to one aspect, a method may further comprise measuring a third value of the light detection signal at a signal period, the signal period being after the first reference period and before the second reference period.

According to one aspect, a method may further comprise computing the measurement signal based on a difference between the average of the first and second values and the third value.

According to other embodiments, a system for magnetic detection may include a magneto-defect center material comprising a plurality of magneto-defect centers, a radio frequency (RF) excitation source configured to provide RF excitation to the magneto-defect center material, an optical excitation source configured to provide optical excitation to the magneto-defect center material, an optical detector configured to receive an optical signal emitted by the magneto-defect center material, a magnetic field generator configured to generate a magnetic field applied to the magneto-defect center material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the magneto-defect center material, receive a light detection signal from the optical detector based on an optical signal emitted by the magneto-defect center material due to the pulse sequence, measure a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the magneto-defect center material, measure a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the magneto-defect center material, and compute a measurement signal based on the measured first and second values.

According to other embodiments, a system for magnetic detection having a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers may include means for providing RF excitation to the NV diamond material, means for providing optical excitation to the NV diamond material, means for receiving an optical signal emitted by the NV diamond material, means for generating a magnetic field applied to the NV diamond material, and means for applying a first pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, means for receiving a first light detection signal based on an optical signal emitted by the NV diamond material due to the first pulse sequence, means for computing a first measurement based on the first light detection signal, means for applying a second pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, means for receiving a second light detection signal based on an optical signal emitted by the NV diamond material due to the second pulse sequence, and means for computing a second measurement based on the second light detection signal. The first measurement may be based on a high resonance frequency of the NV diamond material, and the second measurement may be based on a low resonance frequency of the NV diamond material.

According to other embodiments, a method for detecting a magnetic field acting on a nitrogen vacancy (NV) diamond material comprising a plurality of NV centers may include controlling an optical excitation source and an RF excitation source to apply a first pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receiving a first light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the first pulse sequence, computing a first measurement based on the first detection signal, controlling the optical excitation source and the RF excitation source to apply a second pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the NV diamond material, receiving a second light detection signal from the optical detector based on an optical signal emitted by the NV diamond material due to the second pulse sequence, and computing a second measurement based on the second light detection signal. The first measurement may be based on a high resonance frequency of the NV diamond material, and the second measurement may be based on a low resonance frequency of the NV diamond material.

According to one aspect, a high resonance frequency and a low resonance frequency may be resonance frequencies associated with an axis of an NV center of the NV diamond material.

According to one aspect, a method may further comprise computing a change in an external magnetic field acting on the NV diamond material based on the first and second measurements.

According to other embodiments, a system for magnetic detection may include a magneto-defect center material comprising a plurality of magneto-defect centers, a radio frequency (RF) excitation source configured to provide RF excitation to the magneto-defect center material, an optical excitation source configured to provide optical excitation to the magneto-defect center material, an optical detector configured to receive an optical signal emitted by the magneto-defect center material, a magnetic field generator configured to generate a magnetic field applied to the magneto-defect center material, and a controller. The controller may be configured to control the optical excitation source and the RF excitation source to apply a first pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the magneto-defect center material, receive a first light detection signal from the optical detector based on an optical signal emitted by the magneto-defect center material due to the first pulse sequence, compute a first measurement based on the first detection signal, control the optical excitation source and the RF excitation source to apply a second pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the magneto-defect center material, receive a second light detection signal from the optical detector based on an optical signal emitted by the magneto-defect center material due to the second pulse sequence, and compute a second measurement based on the second light detection signal. The first measurement may be based on a high resonance frequency of the magneto-defect center material, and the second measurement may be based on a low resonance frequency of the magneto-defect center material.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates one orientation of an NV center in a diamond lattice.

FIG. 2 is an energy level diagram showing energy levels of spin states for the NV center.

FIG. 3 is a schematic diagram illustrating a conventional NV center magnetic sensor system.

FIG. 4 is a graph illustrating the fluorescence as a function of an applied RF frequency of an NV center along a given direction for a zero magnetic field.

FIG. 5 is a graph illustrating the fluorescence as a function of an applied RF frequency for four different NV center orientations for a non-zero magnetic field.

FIG. 6 is a schematic diagram illustrating a magnetic field detection system according to an embodiment.

FIG. 7 is a schematic illustrating a Ramsey sequence of optical excitation pulses and RF excitation pulses according to an operation of the system of FIG. 6.

FIG. 8A is a free induction decay curve where a free precession time τ is varied using the Ramsey sequence of FIG. 7.

FIG. 8B is a magnetometry curve where a RF detuning frequency Δ is varied using the Ramsey sequence of FIG. 7.

FIG. 9A is a free induction decay surface plot where both the free precession time τ and the RF detuning frequency Δ are varied using the Ramsey sequence of FIG. 7.

FIG. 9B is a plot showing a gradient of the free induction decay surface plot of FIG. 9B.

FIG. 10 is a schematic illustrating a Rabi sequence of optical excitation pulses and RF pulses according to an operation of the system of FIG. 6.

FIG. 11 is a comparison of graphs showing resonant Rabi frequencies according to a power of RF excitation applied to the system of FIG. 6.

FIG. 12 is a graph showing raw pulse data collected during an operation of the system of FIG. 6.

DETAILED DESCRIPTION

The present disclosure relates to apparatuses and methods for stimulating a NV diamond in a magnetic detection system using an optimized stimulation process to significantly increase magnetic sensitivity of the detection system. The system utilizes a Ramsey pulse sequence to detect and measure the magnetic field acting on the system. Parameters relating to the Ramsey pulse sequence are optimized before measurement of the magnetic field. These parameters include the resonant Rabi frequency, the free precession time (tau), and the detuning frequency, all of which help improve the sensitivity of the measurement. These parameters may be optimally determined using calibration tests utilizing other optical detection techniques, such as a Rabi pulse sequence or additional Ramsey sequences. In addition, parameters, in particular the resonant Rabi frequency, may be further optimized by an increase in power of the RF excitation source, which may be achieved through the use of a small loop antenna. During measurement of the magnetic field, the RF excitation pulses applied during the Ramsey sequences may be set to occur at separate resonance frequencies associated with different spin states (e.g., m_(s)=+1 or m_(s)=−1). By utilizing separate resonance locations, changes due to temperature and/or strain effects in the system and changes due to the external magnetic field may be separated out, thus improving the accuracy of the measurements. Finally, processing of the data obtained during measurement is further optimized by the use of at least two reference windows, the average of which is used to obtain the signal. The above provide a magnetic detection system capable of improved sensitivity in detection of a magnetic field. In some embodiments, the optimized measurement process may result in a sensitivity of the magnetic detection system of about 9 nT/√{square root over (Hz)} or less.

The NV Center, Its Electronic Structure, and Optical and RF Interaction

The NV center in a diamond comprises a substitutional nitrogen atom in a lattice site adjacent a carbon vacancy as shown in FIG. 1. The NV center may have four orientations, each corresponding to a different crystallographic orientation of the diamond lattice.

The NV center may exist in a neutral charge state or a negative charge state. Conventionally, the neutral charge state uses the nomenclature NV⁰, while the negative charge state uses the nomenclature NV, which is adopted in this description.

The NV center has a number of electrons, including three unpaired electrons, each one from the vacancy to a respective of the three carbon atoms adjacent to the vacancy, and a pair of electrons between the nitrogen and the vacancy. The NV center, which is in the negatively charged state, also includes an extra electron.

The NV center has rotational symmetry, and as shown in FIG. 2, has a ground state, which is a spin triplet with ³A₂ symmetry with one spin state m_(s)=0, and two further spin states m_(s)=+1, and m_(s)=−1. In the absence of an external magnetic field, the m_(s)=±1 energy levels are offset from the m_(s)=0 due to spin-spin interactions, and the m_(s)=±1 energy levels are degenerate, i.e., they have the same energy. The m_(s)=0 spin state energy level is split from the m_(s)=±1 energy levels by an energy of 2.87 GHz for a zero external magnetic field.

Introducing an external magnetic field with a component along the NV axis lifts the degeneracy of the m_(s)=±1 energy levels, splitting the energy levels m_(s)=±1 by an amount 2 gμ_(B)Bz, where g is the g-factor, μ_(B) is the Bohr magneton, and Bz is the component of the external magnetic field along the NV axis. This relationship is correct to a first order and inclusion of higher order corrections is a straightforward matter and will not affect the computational and logic steps in the systems and methods described below.

The NV center electronic structure further includes an excited triplet state ³E with corresponding m_(s)=0 and m_(s)=±1 spin states. The optical transitions between the ground state ³A₂ and the excited triplet ³E are predominantly spin conserving, meaning that the optical transitions are between initial and final states that have the same spin. For a direct transition between the excited triplet ³E and the ground state ³A₂, a photon of red light is emitted with a photon energy corresponding to the energy difference between the energy levels of the transitions.

There is, however, an alternative non-radiative decay route from the triplet ³E to the ground state ³A₂ via intermediate electron states, which are thought to be intermediate singlet states A, E with intermediate energy levels. Significantly, the transition rate from the m_(s)=±1 spin states of the excited triplet ³E to the intermediate energy levels is significantly greater than the transition rate from the m_(s)=0 spin state of the excited triplet ³E to the intermediate energy levels. The transition from the singlet states A, E to the ground state triplet ³A₂ predominantly decays to the m_(s)=0 spin state over the m_(s)=±1 spins states. These features of the decay from the excited triplet ³E state via the intermediate singlet states A, E to the ground state triplet ³A₂ allows that if optical excitation is provided to the system, the optical excitation will eventually pump the NV center into the m_(s)=0 spin state of the ground state ³A₂. In this way, the population of the m_(s)=0 spin state of the ground state ³A₂ may be “reset” to a maximum polarization determined by the decay rates from the triplet ³E to the intermediate singlet states.

Another feature of the decay is that the fluorescence intensity due to optically stimulating the excited triplet ³E state is less for the m_(s)=±1 states than for the m_(s)=0 spin state. This is so because the decay via the intermediate states does not result in a photon emitted in the fluorescence band, and because of the greater probability that the m_(s)=±1 states of the excited triplet ³E state will decay via the non-radiative decay path. The lower fluorescence intensity for the m_(s)=±1 states than for the m_(s)=0 spin state allows the fluorescence intensity to be used to determine the spin state. As the population of the m_(s)=±1 states increases relative to the m_(s)=0 spin, the overall fluorescence intensity will be reduced.

The NV Center, or Magneto-Optical Defect Center, Magnetic Sensor System

FIG. 3 is a schematic diagram illustrating a conventional NV center magnetic sensor system 300 that uses fluorescence intensity to distinguish the m_(s)=±1 states, and to measure the magnetic field based on the energy difference between the m_(s)=+1 state and the m_(s)=−1 state. The system 300 includes an optical excitation source 310, which directs optical excitation to an NV diamond material 320 with NV centers. The system further includes an RF excitation source 330, which provides RF radiation to the NV diamond material 320. Light from the NV diamond may be directed through an optical filter 350 to an optical detector 340.

The RF excitation source 330 may be a microwave coil, for example. The RF excitation source 330, when emitting RF radiation with a photon energy resonant with the transition energy between ground m_(s)=0 spin state and the m_(s)=+1 spin state, excites a transition between those spin states. For such a resonance, the spin state cycles between ground m_(s)=0 spin state and the m_(s)=+1 spin state, reducing the population in the m_(s)=0 spin state and reducing the overall fluorescence at resonances. Similarly, resonance occurs between the m_(s)=0 spin state and the m_(s)=−1 spin state of the ground state when the photon energy of the RF radiation emitted by the RF excitation source is the difference in energies of the m_(s)=0 spin state and the m_(s)=−1 spin state, or between the m_(s)=0 spin state and the m_(s)=+1 spin state, there is a decrease in the fluorescence intensity.

The optical excitation source 310 may be a laser or a light emitting diode, for example, which emits light in the green, for example. The optical excitation source 310 induces fluorescence in the red, which corresponds to an electronic transition from the excited state to the ground state. Light from the NV diamond material 320 is directed through the optical filter 350 to filter out light in the excitation band (in the green, for example), and to pass light in the red fluorescence band, which in turn is detected by the detector 340. The optical excitation light source 310, in addition to exciting fluorescence in the diamond material 320, also serves to reset the population of the m_(s)=0 spin state of the ground state ³A₂ to a maximum polarization, or other desired polarization.

For continuous wave excitation, the optical excitation source 310 continuously pumps the NV centers, and the RF excitation source 330 sweeps across a frequency range that includes the zero splitting (when the m_(s)=±1 spin states have the same energy) photon energy of 2.87 GHz. The fluorescence for an RF sweep corresponding to a diamond material 320 with NV centers aligned along a single direction is shown in FIG. 4 for different magnetic field components Bz along the NV axis, where the energy splitting between the m_(s)=−1 spin state and the m_(s)=+1 spin state increases with Bz. Thus, the component Bz may be determined. Optical excitation schemes other than continuous wave excitation are contemplated, such as excitation schemes involving pulsed optical excitation, and pulsed RF excitation. Examples of pulsed excitation schemes include Ramsey pulse sequence (described in more detail below), and spin echo pulse sequence.

In general, the diamond material 320 will have NV centers aligned along directions of four different orientation classes. FIG. 5 illustrates fluorescence as a function of RF frequency for the case where the diamond material 320 has NV centers aligned along directions of four different orientation classes. In this case, the component Bz along each of the different orientations may be determined. These results, along with the known orientation of crystallographic planes of a diamond lattice, allow not only the magnitude of the external magnetic field to be determined, but also the direction of the magnetic field.

While FIG. 3 illustrates an NV center magnetic sensor system 300 with NV diamond material 320 with a plurality of NV centers, in general, the magnetic sensor system may instead employ a different magneto-optical defect center material, with a plurality of magneto-optical defect centers. The electronic spin state energies of the magneto-optical defect centers shift with magnetic field, and the optical response, such as fluorescence, for the different spin states is not the same for all of the different spin states. In this way, the magnetic field may be determined based on optical excitation, and possibly RF excitation, in a corresponding way to that described above with NV diamond material.

FIG. 6 is a schematic diagram of a system 600 for a magnetic field detection system according to an embodiment. The system 600 includes an optical excitation source 610, which directs optical excitation to an NV diamond material 620 with NV centers, or another magneto-optical defect center material with magneto-optical defect centers. An RF excitation source 630 provides RF radiation to the NV diamond material 620. A magnetic field generator 670 generates a magnetic field, which is detected at the NV diamond material 620.

The magnetic field generator 670 may generate magnetic fields with orthogonal polarizations, for example. In this regard, the magnetic field generator 670 may include two or more magnetic field generators, such as two or more Helmholtz coils. The two or more magnetic field generators may be configured to provide a magnetic field having a predetermined direction, each of which provide a relatively uniform magnetic field at the NV diamond material 620. The predetermined directions may be orthogonal to one another. In addition, the two or more magnetic field generators of the magnetic field generator 670 may be disposed at the same position, or may be separated from each other. In the case that the two or more magnetic field generators are separated from each other, the two or more magnetic field generators may be arranged in an array, such as a one-dimensional or two-dimensional array, for example.

The system 600 may be arranged to include one or more optical detection systems 605, where each of the optical detection systems 605 includes the optical detector 640, optical excitation source 610, and NV diamond material 620. Furthermore, the magnetic field generator 670 may have a relatively high power as compared to the optical detection systems 605. In this way, the optical systems 605 may be deployed in an environment that requires a relatively lower power for the optical systems 605, while the magnetic field generator 670 may be deployed in an environment that has a relatively high power available for the magnetic field generator 670 so as to apply a relatively strong magnetic field.

The system 600 further includes a controller 680 arranged to receive a light detection signal from the optical detector 640 and to control the optical excitation source 610, the RF excitation source 630, and the second magnetic field generator 675. The controller may be a single controller, or multiple controllers. For a controller including multiple controllers, each of the controllers may perform different functions, such as controlling different components of the system 600. The second magnetic field generator 675 may be controlled by the controller 680 via an amplifier 660, for example.

The RF excitation source 630 may be a microwave coil, for example. The RF excitation source 630 is controlled to emit RF radiation with a photon energy resonant with the transition energy between the ground m_(s)=0 spin state and the m_(s)=±1 spin states as discussed above with respect to FIG. 3.

The optical excitation source 610 may be a laser or a light emitting diode, for example, which emits light in the green, for example. The optical excitation source 610 induces fluorescence in the red from the NV diamond material 620, where the fluorescence corresponds to an electronic transition from the excited state to the ground state. Light from the NV diamond material 620 is directed through the optical filter 650 to filter out light in the excitation band (in the green, for example), and to pass light in the red fluorescence band, which in turn is detected by the optical detector 640. The optical excitation light source 610, in addition to exciting fluorescence in the NV diamond material 620, also serves to reset the population of the m_(s)=0 spin state of the ground state ³A₂ to a maximum polarization, or other desired polarization.

The controller 680 is arranged to receive a light detection signal from the optical detector 640 and to control the optical excitation source 610, the RF excitation source 630, and the second magnetic field generator 675. The controller may include a processor 682 and a memory 684, in order to control the operation of the optical excitation source 610, the RF excitation source 630, and the second magnetic field generator 675. The memory 684, which may include a nontransitory computer readable medium, may store instructions to allow the operation of the optical excitation source 610, the RF excitation source 630, and the second magnetic field generator 675 to be controlled. That is, the controller 680 may be programmed to provide control.

Ramsey Pulse Sequence Overview

According to certain embodiments, the controller 680 controls the operation of the optical excitation source 610, the RF excitation source 630, and the magnetic field generator 670 to perform Optically Detected Magnetic Resonance (ODMR). The component of the magnetic field Bz along the NV axis of NV centers aligned along directions of the four different orientation classes of the NV centers may be determined by ODMR, for example, by using an ODMR pulse sequence according to a Ramsey pulse sequence. The Ramsey pulse sequence is a pulsed RF-pulsed laser scheme that measures the free precession of the magnetic moment in the NV diamond material 620 and is a technique that quantum mechanically prepares and samples the electron spin state.

FIG. 7 is a schematic diagram illustrating the Ramsey pulse sequence. As shown in FIG. 7, a Ramsey pulse sequence includes optical excitation pulses and RF excitation pulses over a five-step period. In a first step, during a period 0, a first optical excitation pulse 710 is applied to the system to optically pump electrons into the ground state (i.e., m_(s)=0 spin state). This is followed by a first RF excitation pulse 720 (in the form of, for example, a microwave (MW) π/2 pulse) during a period 1. The first RF excitation pulse 720 sets the system into superposition of the m_(s)=0 and m_(s)=+1 spin states (or, alternatively, the m_(s)=0 and m_(s)=−1 spin states, depending on the choice of resonance location). During a period 2, the system is allowed to freely precess (and dephase) over a time period referred to as tau (τ). During this free precession time period, the system measures the local magnetic field and serves as a coherent integration. Next, a second RF excitation pulse 740 (in the form of, for example, a MW π/2 pulse) is applied during a period 3 to project the system back to the m_(s)=0 and m_(s)=+1 basis. Finally, during a period 4, a second optical pulse 730 is applied to optically sample the system and a measurement basis is obtained by detecting the fluorescence intensity of the system. The RF excitation pulses applied to the system 600 are provided at a given RF frequency, which correspond to a given NV center orientation. The Ramsey pulse sequence shown in FIG. 12 may be performed multiple times, wherein each of the MW pulses applied to the system during a given Ramsey pulse sequence includes a different frequency that respectively corresponds to a different NV center orientation.

The theoretical measurement readout from a Ramsey pulse sequence may be defined as equation (1) below:

$\begin{matrix} {1 - {e^{\frac{\tau}{T_{2}^{*}}} \star \left( \frac{\omega_{res}}{\omega_{eff}} \right)^{2} \star {\sum\limits_{m = {- 1}}^{1}{\cos\left( {\left( {2{\pi\left( {\Delta + {m \star \alpha_{n}}} \right)}} \right) \star \left( {\tau + \theta} \right)} \right)}}}} & (1) \end{matrix}$

In equation (1) above, τ represents the free precession time, T₂* represents spin dephasing due to inhomogeneities present in the system 600, ω_(res) represents the resonant Rabi frequency, ω_(eff) represents the effective Rabi frequency, a_(n) represents the hyperfine splitting of the NV diamond material 620 (˜2.14 MHz), A represents the MW detuning, and θ represents the phase offset.

When taking a measurement based on a Ramsey pulse sequence, the parameters that may be controlled are the duration of the MW π/2 pulses, the frequency of the MW pulse (which is referenced as the frequency amount detuned from the resonance location, Δ), and the free precession time τ. FIGS. 8A and 8B show the effects on the variance of certain parameters of the Ramsey pulse sequence. For example, as shown in FIG. 8A, if all parameters are kept constant except for the free precession time τ, an interference pattern, known as the free induction decay (FID), is obtained. The FID curve is due to the constructive/destructive interference of the three sinusoids that correspond to the hyperfine splitting. The decay of the signal is due to inhomogeneous dephasing and the rate of this decay is characterized by T₂* (characteristic decay time). In addition, as shown in FIG. 8B, if all parameters are kept constant except for the microwave detuning Δ, a magnetometry curve is obtained. In this case, the x-axis may be converted to units of magnetic field through the conversion 1 nT=28 Hz in order to calibrate for magnetometry.

By varying both τ and Δ, a two-dimensional FID surface plot may be constructed, an example of which is shown in FIG. 9A. The FID surface plot includes several characteristics that can elucidate optimization of the controllable parameters of the Ramsey sequence. For example, in FIG. 9A, the FID surface plot is generated using a T₂* of about 750 ns and a resonant Rabi frequency of about 6.25 MHz. The horizontal slices of FIG. 9A represent individual FID curves (e.g., FIG. 8A), while the vertical slices represent magnetometry curves (e.g., FIG. 8B). As shown in FIG. 9A, FID curves of higher fundamental frequency occur at greater detuning. Thus, higher detuning frequencies may be used to fit T₂* for diamond characterization. In addition, magnetometry curves, such as that shown in FIG. 8B, demonstrate that certain areas generate greater sensitivities. In particular, by taking the gradient of a two-dimensional FID surface plot, discreet optimal free precession intervals may be identified that present greater sensitivities, the best of which will be determined by T₂*. FIG. 9B shows the gradient of the two-dimensional FID surface plot of FIG. 9A. In FIG. 9B, for the particular T₂* used (i.e., about 750 ns), operating at around 900 ns (indicated by area 2 of FIG. 9B) will yield the greatest sensitivity. However, shorter T₂* will show better performance between about 400 ns and about 500 ns (indicated by area 1 of FIG. 9B), while longer T₂* will show better performance at around 1400 ns (indicated by area 3 of FIG. 9B). These strong interference regions indicated by a plot such as that shown in FIG. 9B allow for the optimization of τ that will yield greater measurement sensitivity.

In addition, while the decay in the horizontal axis of FIG. 9B is characterized by T₂*, the decay in the vertical axis is characterized by the ratio of the resonant Rabi frequency ω_(res) (described in more detail below) to the effective Rabi frequency ω_(eff). The effective Rabi frequency may be defined by equation (2) below: ω_(eff):=√{square root over (ω_(res) ²+Δ²)}  (2)

Thus, the ratio of the resonant Rabi frequency and the effective Rabi frequency may be expressed in terms of the resonant Rabi frequency, as follows:

$\begin{matrix} {\frac{\omega_{res}}{\omega_{eff}} = \frac{\omega_{res}}{\sqrt{\omega_{res}^{2} + \Delta^{2}}}} & (3) \end{matrix}$

As shown in equation (3) above, when the resonant Rabi frequency ω_(res) is much greater than the MW detuning Δ, the ratio of the resonant Rabi frequency to the effective Rabi frequency will be about equal to 1. The decay shown in the vertical axis of FIG. 9B may be partially controlled by RF excitation power. As will be described in greater detail below, as the RF excitation power increases, a greater resonant Rabi frequency may be realized, while also decreasing the percent change in the effective Rabi frequency due to detuning. Thus, according to certain embodiments, magnetometry measurements are operated in regions that are dominated by the resonant Rabi frequency (such that the ratio of equation (3) is close to 1) in order to achieve maximum contrast.

Measurement Sequence

Using the above observations, a general three-step approach may be used to obtain highly sensitive magnetometry measurements. In this general approach, a first step is performed to verify the resonant Rabi frequency ω_(res). In a second step, the inhomogeneous dephasing T₂* of the system is measured. Finally, using the measurements obtained in the first and second steps, the parameter space of equation (1) is optimized and a highly sensitivity magnetometry measurement is performed. These three steps are described in more detail below.

Measuring the Resonant Rabi Frequency

To verify the resonant Rabi frequency, first, a bias magnetic field using the magnetic field generator 670 is applied to the system 600 such that the outermost resonance of the fluorescence intensity response is separated, while the three remaining resonances for the other axes remain overlapping. Next, either a CW-CW sweep or a single π pulse sweep is applied to identify the resonance RF frequency that corresponds to the axis of interest (i.e., the outermost resonance). Then, while tuned to this resonance, a series of Rabi pulses is applied. FIG. 10 shows an example of a Rabi pulse sequence. As shown in FIG. 10, three periods of optical and RF excitation pulses are applied. First, a first optical excitation pulse 810 is applied, which is followed by a RF excitation pulse 820 (e.g., a MW pulse). The Rabi pulse sequence is then completed by a second optical excitation pulse 830. During application of the series of Rabi pulses, the time interval in which the RF pulse is applied (shown as tau τ in FIG. 10, but this tau τ should be distinguished from the free precession interval τ in a Ramsey pulse sequence) is varied. During this process, a constant optical duty cycle is maintained to minimize thermal effects in the system. This may be achieved with the use of a variable “guard” window, shown as the period 850 in FIG. 10, between the first optical pulse 810 and the MW pulse 820. The guard window 850 helps to ensure that the first optical pulse 810 is completely off by the time the MW pulse 820 is applied, thus preventing any overlap between the two pulses and preventing the optical pulse from partially re-initializing the NV diamond material while the MW pulse 820 is being applied.

After application of the Rabi pulses, the resonant Rabi frequency ω_(res) is defined by the frequency of the resulting curve. FIG. 11 shows measured curves A-D after the application of the Rabi pulses using varying RF excitation power (e.g., MW power). As shown by the differences in the frequency of curves A-D, by increasing the MW power applied to the system 600, the resonant Rabi frequency ω_(res) obtained also increases. Thus, to obtain practical Rabi frequencies (e.g., greater than 5 MHz), substantial amounts of MW power should be used. In some embodiments, sufficient MW power may be applied to ensure that application of the pulses is kept short, while, at the same time, the MW power may be limited to avoid saturation. In certain embodiments, a power of about 10 watts may be applied. Depending on the RF excitation source 630 used to apply the RF excitation, the necessary power requirements to achieve practical Rabi frequencies may be difficult to achieve. In certain embodiments, however, a small loop antenna (e.g., an antenna having a loop size of about 2 mm in diameter) may be used as the RF excitation source 630. By applying a small loop antenna, a high MW power may be achieved while significantly reducing the required antenna power due to the ability to position the antenna in closer proximity to the NV diamond material 620. Thus, the increase in MW power achieved by the small loop antenna allows for an increase in the resonant Rabi frequency ω_(res). The data obtained during this step of the measurement process is used to determine the π/2 pulse necessary to perform the Ramsey pulse sequence (described below). In this case, π may be defined as the first minimum of the Rabi curve obtained (e.g., curve D in FIG. 11).

Measuring T2*

In a second step of the measurement process, using the π/2 pulse determined by the resonant Rabi frequency and the resonance location obtained during the first step above, measurements of the inhomogeneous dephasing T₂* of the system are obtained. Measurements are performed similar to the Rabi measurements described above, except a Ramsey pulse sequence is used. As described above with reference to the Ramsey pulse sequence, tau τ denotes the free precession time interval in this step.

In estimating T₂*, the detune frequency Δ is set to be relatively high, in certain embodiments. As noted above, larger detune frequencies cause higher fundamental frequencies (see, e.g., FIG. 9A), thus allowing for greater contrast, making the data easier to fit. In some embodiments, the detune frequency Δ may be set to about 10 MHz. However, for relatively large T₂*, smaller detune frequencies may be used. FIG. 8A shows one example of an FID curve that may be used to obtain T₂*, where the detune frequency was set to about 10 MHz. By determining T₂* from an FID curve such as that shown in FIG. 8A, the optimal free precession time τ may be determined based on the strong interference regions discussed above with reference to FIG. 9B. In addition, in certain embodiments, a small range of τ's are also collected on either side of the optimally determined free precession time due to the theta term in equation (1).

Magnetometry Measurements

In the final step of the measurement process, measurement of the fluorescence intensity response is performed using the parameters obtained in the above steps. As discussed above, the identified resonant Rabi frequency gives the duration of the MW π/2 pulse (used as RF excitation pulses 720 and 740), and the FID curve gives T₂*, which is used to determine the region of optimal free precession time τ. It should be noted that, during this final step, in some embodiments, the optical pulse used for optical polarization of the system and the optical pulse used for measurement readout may be merged into one pulse during application of a series of Ramsey sequences.

In addition, in order to increase sensitivity, measurements made in a second per fixed measurement error may be increased in certain embodiments. Thus, to maximize sensitivity, the total length of a single measurement cycle should be minimized, which may be achieved through the use of higher optical powers of the optical excitation source 610. Accordingly, given the above, in certain embodiments, the optical power of the optical excitation source 610 may be set to about 1.25 W, the MW π/2 pulse may be applied for about 50 ns, the free precession time τ may be about 420 ns, and the optical excitation pulse duration may be about 50 μs. Moreover, “guard” windows may be employed before and after the MW π/2 pulses, which may be set to be about 2.28 μs and 20 ns in duration, respectively.

In conventional measurement processes, the curve in the intensity response is typically only measured once to obtain the slope and fine-tuned frequency, and additional measurements are only taken at the optimal detuning frequency, while the fluorescence signal is monitored. However, the system may experience drift caused by, for example, optical excitation heating (e.g., laser-induced heating) and/or strain, which can contribute to imprecision and error during the measurement process. Tracking a single spin resonance does not properly account for the translation in response curves due to thermal effects. Thus, according to some embodiments, to account for nonlinearities over a larger band of magnetic fields, data obtained from the measuring process is saved in real-time and sensitivity is determined offline to minimize time between measurements. In addition, magnetometry curves are collected on both the m_(s)=+1 and m_(s)=−1 spin states for the same NV symmetry axis. For example, in certain embodiments, RF excitation pulses during the Ramsey sequences may be alternatively applied at low resonance (i.e., resonance frequency of the m_(s)=−1 spin state) and at high resonance (i.e., resonance frequency of the m_(s)=+1 spin state) to obtain measurements associated with each of the spin states (m_(s)=−1 and m_(s)=+1 spin states). Thus, two magnetometry curves (e.g., FIG. 8B) may be obtained for both the positive and negative spin states. By applying the RF pulses at separate frequencies, translation due to temperature and/or strain effects may be compensated. The magnetic field measurements may be made using equations (4) and (5) below, where I represents the normalized intensity of the fluorescence (e.g., red) and m₁ and m₂ represent the measurements taken for each of the m_(s)=+1 and m_(s)=−1 spin states for a given axis:

$\begin{matrix} {m = \frac{d\; l}{d\; f}} & (4) \\ {{d\; B} = {\frac{h}{2g\;\mu\; b}\left( {\frac{d\; I_{1}}{m_{1}} \mp \frac{d\; I_{2}}{m_{2}}} \right)}} & (5) \end{matrix}$

For measurements obtained on opposite slopes, plus is used in equation (5). If the peaks of the m_(s)=+1 and m_(s)=−1 spin states translate, the intensity response will occur in opposite directions. If, on the other hand, the peaks separate outward due to a change in the magnetic field, then the intensity change will agree to yield the appropriate dB measurement. Thus, by obtaining measurements of the curves for both the m_(s)=+1 and m_(s)=−1 spin states for the same NV symmetry axis, changes due to temperature and changes due to the magnetic field may be separated. Accordingly, translation shifts due to temperature and/or strain effects may be accounted for, allowing for a more accurate calculation of the magnetic field contribution on the system.

Signal Processing

Processing may be performed on the raw data obtained to acquire clean images of the measurements obtained during each of the steps described above. FIG. 12 shows an example of a raw pulse data segment that may be obtained during a given measurement cycle. Theoretically, the signal is defined as the first 300 ns of an optical excitation pulse. However, this definition applies at optical power densities that are near saturation. As optical power density decreases from saturation, the useful part of the signal may extend further in time. Currently, in conventional processing methods, the end of the pulse, when the system has been polarized, is referenced in order to account for power fluctuations in the optical excitation source (e.g., the laser). This is shown in FIG. 12, where the signal may be obtained using a first reference window or period defined by C minus a signal window or period defined by B (i.e., signal=C−B), which are both referenced after the MW pulse. According to certain embodiments, however, in order to increase sensitivity, the reference may be extended to include a second reference window or period defined by A before the microwave pulse

$\left( {{i.e.},{{signal} = {\frac{A + C}{2} - B}}} \right).$ The samples within the windows or periods (i.e., A, B, and C) may be averaged to obtain a mean value of the signal contained within the respective window or period. Furthermore, in some embodiments, the value of the windows or periods (e.g., signal window B) may be determined using a weighted mean. In addition, in certain embodiments, the first and second reference windows are equally spaced from the signal window, as shown in FIG. 12. This extension of referencing allows for better estimation of the optical excitation power during the acquisition of the signal and an overall increase in sensitivity of the system.

The embodiments of the inventive concepts disclosed herein have been described in detail with particular reference to preferred embodiments thereof, but it will be understood by those skilled in the art that variations and modifications can be effected within the spirit and scope of the inventive concepts. 

What is claimed is:
 1. A method for detecting a magnetic field acting on a magneto-optical defect center material comprising a plurality of magneto-optical defect centers, comprising: controlling an optical excitation source and an RF excitation source to apply a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the magneto-optical defect center material; receiving a light detection signal from an optical detector based on an optical signal emitted by the magneto-optical defect center material due to the pulse sequence; measuring a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the magneto-optical defect center material; measuring a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the magneto-optical defect center material; computing a measurement signal based on the measured first and second values; and measuring a third value of the light detection signal at a signal period, the signal period being after the first reference period and before the second reference period.
 2. A method for detecting a magnetic field acting on a magneto-optical defect center material comprising a plurality of magneto-optical defect centers, comprising: controlling an optical excitation source and an RF excitation source to apply a pulse sequence comprising two optical excitation pulses and two RF excitation pulses to the magneto-optical defect center material; receiving a light detection signal from an optical detector based on an optical signal emitted by the magneto-optical defect center material due to the pulse sequence; measuring a first value of the light detection signal at a first reference period, the first reference period being before a period of the light detection signal associated with the two RF excitation pulses provided to the magneto-optical defect center material; measuring a second value of the light detection signal at a second reference period, the second reference period being after the period of the light detection signal associated with the two RF excitation pulses provided to the magneto-optical defect center material; computing a measurement signal based on the measured first and second values; measuring a third value of the light detection signal at a signal period, the signal period being after the first reference period and before the second reference period; and comprising computing the measurement signal based on a difference between the average of the first and second values and the third value. 